After creating an account on the website, login in to your new account, and make sure to click the Join The Beta button.
Once you are signed in to the beta, you'll be given a beta key during one of the invite waves. Make sure to keep an eye on your e-mail to see if you got in!
Next, sign in to Steam, and go to Games -> Activate a Product on Steam...
Follow the steam dialogs and enter the game key when prompted. The game should download after activation succeeds.
After Steam finishes downloading, click Play to log in to your account and play Salt the Earth!
Once the game is open, login with your user name and password. The game will initially ask if you want to connect this account with this steam key. Click yes, and login in one last time to begin your beta testing!